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Issue 31, 2016
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Numerical density-to-potential inversions in time-dependent density functional theory

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Abstract

We treat the density-to-potential inverse problem of time-dependent density functional theory as an optimization problem with a partial differential equation constraint. The unknown potential is recovered from a target density by applying a multilevel optimization method controlled by error estimates. We employ a classical optimization routine using gradients efficiently computed by the discrete adjoint method. The inverted potential has both a real and imaginary part to reduce reflections at the boundaries and other numerical artifacts. We demonstrate this method on model one-dimensional systems. The method can be straightforwardly extended to a variety of numerical solvers of the time-dependent Kohn–Sham equations and to systems in higher dimensions.

Graphical abstract: Numerical density-to-potential inversions in time-dependent density functional theory

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Publication details

The article was received on 15 Jan 2016, accepted on 10 Mar 2016 and first published on 17 Mar 2016


Article type: Paper
DOI: 10.1039/C6CP00312E
Citation: Phys. Chem. Chem. Phys., 2016,18, 21079-21091
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    Numerical density-to-potential inversions in time-dependent density functional theory

    D. S. Jensen and A. Wasserman, Phys. Chem. Chem. Phys., 2016, 18, 21079
    DOI: 10.1039/C6CP00312E

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